n 次中心对称量子图的可约性
Reducibility of n Subcentrally Symmetric Quantum Graphs
摘要: 本文根据群的不可约表示给出了 n 次中心对称量子图上平方可积函数空间的分解及 n 次中心对称 量子图的商图，为量子图久期行列式的分解提供了新的思路，将原量子图的谱问题转化为商图的 谱问题，为等谱量子图的研究打下基础。
Abstract: In this paper, according to the irreducible representation of the group, the decompo- sitions of the space of square integrable functions on n subcenter-symmetric quantum graphs and the quotient graph of n subcenter-symmetric quantum graphs are given. It provides a new idea for the decomposition of the long determinant of quantum graphs, and transforms the spectrum problem of the original quantum graph into the spectrum problem of the quotient graph, which lays a foundation for the research of isospectral quantum graphs.
文章引用：张凯, 赵佳. n 次中心对称量子图的可约性[J]. 应用数学进展, 2024, 13(4): 1862-1874. https://doi.org/10.12677/AAM.2024.134175

参考文献

[1] Brooks, H. (1940) Diamagnetic Anisotropy and Electronic Structure of AROMATIC Molecules. The Journal of Chemical Physics, 8, 939-949.
https://doi.org/10.1063/1.1750608
[2] Carlson, R. (2000) Nonclassical Sturm-Liouville Problems and Schro¨dinger Operators on Radial Trees. Electronic Journal of Differential Equations, 71, 1-24.
[3] Solomyak, M. (2003) On the Spectrum of the Laplacian on Regular Metric Trees. Waves in Random Media, 14, 155-171.
https://doi.org/10.1088/0959-7174/14/1/017
[4] Zhao, J., Shi, G.L. and Yan, J. (2018) The Discrete Spectrum of Schro¨dinger Operators with δ-Type Conditions on Regular Metric Trees. Journal of Spectral Theory, 8, 459-491.
https://doi.org/10.4171/jst/202
[5] 赵佳. 无穷度量图上Sturm-Liouville算子的谱性质[D]: [博士学位论文]. 天津: 天津大学, 2016.
[6] Steinberg, B. (2012) Representation Theory of Finite Groups: An Introductory Approach. Springer, New York.
https://doi.org/10.1007/978-1-4614-0776-8
[7] Band, R., Parzanchevski, O. and Ben-Shach, G. (2009) The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums. Journal of Physics A: Mathematical and Theoretical, 42, Article 175202.
https://doi.org/10.1088/1751-8113/42/17/175202
[8] Parzanchevski, O. and Band, R. (2010) Linear Representations and Isospectrality with Boundary Conditions. Journal of Geometric Analysis, 20, 439-471.
https://doi.org/10.1007/s12220-009-9115-6
[9] Liu, W. (2016) Degeneracies in the Eigenvalue Spectrum of Quantum Graphs. Doctoral Thesis, TexasAM University, College Station, TX.
[10] Berkolaiko, G. (2017) An Elementary Introduction to Quantum Graphs. Geometric and Computa- tional Spectral Theory, 700, 41-72.
https://doi.org/10.1090/conm/700/14182

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